I think Mario/Bowser is the longest running rivalry (correct me if I'm wrong), but these two have been going at it to the death for years. Ridley has been in every metroid game as either classic, Meta-, or Omega, and in Metroid: Fusion the X-Parasite mimics him.

I know he is as much an icon as Samus, but sometimes I'm like "FOR F*** SAKE! WHY WON'T YOU JUST DIE?!?!?"